Past Questions

Step-by-step calculation: 1. Find the total Marked Price (MP) of the books: There are 10 books, and each is priced at ₹ 300. Total MP = 10 × 300 = ₹ 3,000. 2. Identify the Selling Price (SP): The books are sold for a total of ₹ 2,500. 3. Calculate the Discount amount: Discount = Total MP - Total SP = 3,000 - 2,500 = ₹ 500. 4. Calculate the Discount Percentage: Discount % = (Discount / Total MP) × 100 Discount % = (500 / 3,000) × 100 Discount % = (1 / 6) × 100 = 100/6 % = 50/3 %. 5. Convert the improper fraction to a mixed fraction: 50 ÷ 3 = 16 with a remainder of 2. Therefore, 50/3% = 16 2/3%. Comparing with options: - Option (a) 16 2/3% matches our calculation. - Option (b) 17 1/2% is incorrect. - Option (c) 3 1/3% is incorrect. - Option (d) 0% is incorrect as there is a clear difference between MP and SP.

A URL (Uniform Resource Locator) is a standardized naming convention used to identify and locate a specific resource (such as an HTML page, an image, a PDF, or a video) on the internet. It consists of several parts: the protocol (e.g., http, https), the domain name (e.g., www.example.com), and often a path to a specific file or directory. Why other options are incorrect: - Option (a): A browser is a software application (like Chrome or Firefox); it is not identified by a URL. - Option (b): While a URL points to a resource hosted on a server, the 'linking' process (mapping a domain to an IP address) is handled by the DNS (Domain Name System), not the URL itself. - Option (d): Server configuration involves settings like memory allocation, security rules, and software versions, which are managed via configuration files (e.g., .htaccess or nginx.conf), not by the URL.

Step-by-step solution: 1. **Determine individual work rates**: - A's rate = 1/6 of the work per day. - B's rate = 1/8 of the work per day. 2. **Determine the combined work rate**: - A, B, and C together complete the work in 3 days, so their combined rate is 1/3 of the work per day. 3. **Set up the equation to find C's rate**: Let C's rate be 1/x. Rate of A + Rate of B + Rate of C = Combined Rate (1/6) + (1/8) + (1/x) = 1/3 4. **Solve for 1/x**: - Find a common denominator for 1/6 and 1/8, which is 24. - (4/24) + (3/24) + (1/x) = 1/3 - (7/24) + (1/x) = 1/3 - 1/x = 1/3 - 7/24 - 1/x = 8/24 - 7/24 - 1/x = 1/24 5. **Calculate the time for C**: Since C's rate is 1/24 of the work per day, C alone can complete the work in 24 days. Comparing this to the options: - Option (a) 12 days is incorrect. - Option (b) 18 days is incorrect. - Option (c) 24 days is correct. - Option (d) 32 days is incorrect.

Let the time spent travelling on the bicycle be 't' hours. Since the total time taken is 9 hours, the time spent travelling on foot must be (9 - t) hours. We know that Distance = Speed × Time. 1. Distance travelled on bicycle = 9 km/hr × t = 9t km 2. Distance travelled on foot = 4 km/hr × (9 - t) = (36 - 4t) km The total distance travelled is given as 61 km. Therefore: 9t + (36 - 4t) = 61 5t + 36 = 61 5t = 61 - 36 5t = 25 t = 5 hours Now, we calculate the distance travelled on the bicycle: Distance = 9 km/hr × 5 hours = 45 km. Verification: Distance on foot = 4 km/hr × (9 - 5) = 4 × 4 = 16 km. Total distance = 45 km + 16 km = 61 km. This matches the question statement. Comparing with options: a. 40km (Incorrect) b. 36km (Incorrect) c. 30km (Incorrect) d. 45km (Correct)

To find the volume of a room (which is typically a rectangular prism or cuboid), the formula used is: Volume = Base Area × Height. Given: 1. Base Area = 16 m² 2. Height = 3 m Calculation: Volume = 16 m² × 3 m = 48 m³. Analysis of options: - Option (a) 16m: Incorrect value and incorrect unit (length instead of volume). - Option (b) 48m³: Correct value and correct unit (cubic meters). - Option (c) 54m: Incorrect value and incorrect unit. - Option (d) 66m³: Incorrect value.

Step-by-step solution: 1. Let the initial salaries of Remi and Sawmi be 2x and 3x respectively, based on the given ratio 2:3. 2. According to the problem, both salaries are increased by ₹ 4000. The new salaries are (2x + 4000) and (3x + 4000). 3. The new ratio is given as 40:57. We can set up the following equation: (2x + 4000) / (3x + 4000) = 40 / 57 4. Cross-multiply to solve for x: 57 * (2x + 4000) = 40 * (3x + 4000) 114x + 228,000 = 120x + 160,000 5. Rearrange the terms to isolate x: 228,000 - 160,000 = 120x - 114x 68,000 = 6x x = 68,000 / 6 x = 11,333.33... 6. Now, calculate Sawmi's initial salary (3x): Sawmi's Salary = 3 * (68,000 / 6) = 68,000 / 2 = ₹ 34,000. 7. However, the question asks for Sawmi's salary. Usually, in such competitive exam contexts, if the options don't match the 'initial' salary, we check for the 'new' salary after the increase: New Salary = 34,000 + 4,000 = ₹ 38,000 (This matches option a). Wait, let's re-verify the calculation. If Sawmi's initial salary was 34,000 and Remi's was 22,666.66, the ratio is 2:3. New salaries: Remi = 26,666.66, Sawmi = 38,000. Ratio: 26,666.66 / 38,000 = 0.7017. Target ratio: 40/57 = 0.70175. Let's re-read the options. If the answer is ₹ 46,800 (Option b): If Sawmi's new salary = 46,800, then initial = 42,800. If Sawmi's initial = 46,800, then new = 50,800. Let's test Option b (₹ 46,800) as the initial salary: If Sawmi = 46,800 (3x), then x = 15,600. Remi = 2x = 31,200. New Remi = 31,200 + 4,000 = 35,200. New Sawmi = 46,800 + 4,000 = 50,800. Ratio = 35,200 / 50,800 = 352 / 508 = 88 / 127 (Not 40/57). Let's re-calculate the equation: 114x + 228,000 = 120x + 160,000 6x = 68,000 3x = 34,000. Sawmi's initial salary = 34,000. Sawmi's new salary = 38,000. Given the options provided in the prompt, Option (a) ₹ 38,000 matches the salary after the increase. However, if the question intended a different ratio or value, we must check the options again. If we assume the ratio was meant to be different or there is a typo in the question's provided options vs the math, based on the provided numbers, 38,000 is the only mathematically reachable figure. Correction: Let's check if Sawmi's salary is the 'new' salary. If New Sawmi = 38,000, then Initial Sawmi = 34,000. Initial Remi = (2/3)*34,000 = 22,666.66. New Remi = 26,666.66. Ratio = 26,666.66 / 38,000 = 40/57. This confirms Option (a) is the New Salary. Wait, looking at the options again, if the answer is (b) 46,800, let's reverse engineer: (2x+4000)/(3x+4000) = 40/57 57(2x+4000) = 40(3x+4000) 114x + 228000 = 120x + 160000 6x = 68000 3x = 34000. New salary = 38000. There might be a typo in the provided options or the question's ratio. But based on the calculation, 38,000 is the correct result for the new salary. If the question asks for 'Sawmi's salary' and 38,000 is an option, it refers to the salary after the increase.

Let the height of the tower be 'h' and the length of the shadow when the altitude is 60° be 'x'. 1. When the altitude of the sun is 60°: tan(60°) = height / shadow √3 = h / x h = x√3 --- (Equation 1) 2. When the altitude of the sun is 30°: The shadow length increases by 30m, so the shadow is (x + 30). tan(30°) = height / shadow 1/√3 = h / (x + 30) h = (x + 30) / √3 --- (Equation 2) 3. Equating the two expressions for h: x√3 = (x + 30) / √3 Multiply both sides by √3: x(√3 * √3) = x + 30 3x = x + 30 2x = 30 x = 15m 4. Substitute x back into Equation 1 to find the height (h): h = 15 * √3 = 15√3 m. Therefore, the height of the tower is 15√3 m. Note: Options (a) and (c) are identical in the provided list; both represent the correct numerical value.

To solve this puzzle, we map the friends to their colors and professions based on the given clues: 1. **Rosy**: Likes Yellow and is a Student (Given in clue 1). 2. **Mary**: Likes Purple (Given in clue 3). She is not a Teacher (Given in clue 3). 3. **Andy**: Likes Blue (Given in clue 3). Clue 4 states the Inspector likes Blue, so Andy is the Inspector. 4. **Lily**: Likes Brown (Given in clue 4). 5. **Daisy**: The only person left. The only color left is Green (since Yellow, Purple, Blue, and Brown are taken). Therefore, Daisy likes Green. Clue 2 states the Librarian likes Green, so Daisy is the Librarian. Now let's determine the remaining professions (Teacher and Principal) for Mary and Lily: - Mary is not a Teacher (Clue 3), so Mary must be the Principal. - Lily is the only one left to be the Teacher. Summary Table: - Rosy: Yellow | Student - Mary: Purple | Principal - Andy: Blue | Inspector - Lily: Brown | Teacher - Daisy: Green | Librarian Evaluating the options: - a. Andy - Inspector: Correct pair. - b. Purple - Principal: Correct pair (Mary likes Purple and is the Principal). - c. Daisy - Green: Correct pair. - d. Rosy - Teacher: Wrong pair. Rosy is a Student, not a Teacher.

Option A is correct: 130m.

Step-by-step solution: 1. **Identify given values and unify units**: - Radius of sphere ($R$) = 2.1 dm = 21 cm. - Length (height) of cylinder ($h$) = 7 cm. 2. **Calculate Volume of the Sphere**: - Volume of sphere = $\frac{4}{3} \pi R^3$ - Volume = $\frac{4}{3} \pi (21)^3$ cm³. 3. **Find the radius of the cylinder ($r$)**: - Since the sphere is converted into a cylinder, their volumes are equal. - Volume of cylinder = $\pi r^2 h$ - $\pi r^2 (7) = \frac{4}{3} \pi (21)^3$ - $r^2 = \frac{4 \times 21 \times 21 \times 21}{3 \times 7}$ - $r^2 = 4 \times 21 \times 21 = (2 \times 21)^2 = 42^2$ - $r = 42$ cm. 4. **Calculate Total Surface Area (TSA) of the Sphere**: - $TSA_{sphere} = 4 \pi R^2 = 4 \pi (21)^2 = 4 \pi (441) = 1764\pi$ cm². 5. **Calculate Total Surface Area (TSA) of the Cylinder (Rod)**: - $TSA_{cylinder} = 2\pi r(r + h)$ - $TSA_{cylinder} = 2\pi (42)(42 + 7) = 2\pi (42)(49)$ - $TSA_{cylinder} = 84 \times 49 \pi = 4116\pi$ cm². 6. **Calculate the Ratio**: - Ratio = $\frac{TSA_{cylinder}}{TSA_{sphere}} = \frac{4116\pi}{1764\pi}$ - Dividing both by 588: $4116 / 588 = 7$ and $1764 / 588 = 3$. - Ratio = 7:3. Therefore, the correct option is (d) 7:3.

To find the missing number in the sequence 7, 26, 63, 124, 215, 342, (...), we look for a mathematical pattern relating the numbers. Observation: - The first number is 7, which is close to 8 (2³). - The second number is 26, which is close to 27 (3³). - The third number is 63, which is close to 64 (4³). - The fourth number is 124, which is close to 125 (5³). - The fifth number is 215, which is close to 216 (6³). - The sixth number is 342, which is close to 343 (7³). The pattern is clearly (n³ - 1), starting from n = 2: 1. 2³ - 1 = 8 - 1 = 7 2. 3³ - 1 = 27 - 1 = 26 3. 4³ - 1 = 64 - 1 = 63 4. 5³ - 1 = 125 - 1 = 124 5. 6³ - 1 = 216 - 1 = 215 6. 7³ - 1 = 343 - 1 = 342 Following this pattern, the next number (the 7th term) should be based on n = 8: 7. 8³ - 1 = 512 - 1 = 511 Comparing this result to the options: a. 391 (Incorrect) b. 421 (Incorrect) c. 481 (Incorrect) d. 511 (Correct)

To find the percentage change in the area of a square when its sides are increased, we can use two methods: the formula method or the assumption method. Method 1: Using the Successive Percentage Formula When two dimensions of a shape (like length and width of a rectangle or sides of a square) are increased, the net percentage change in area is given by the formula: Net % Change = a + b + (ab / 100) Here, a = 25% and b = 25% (since it is a square, both sides increase by the same percentage). Net % Change = 25 + 25 + (25 * 25 / 100) Net % Change = 50 + (625 / 100) Net % Change = 50 + 6.25 = 56.25% Method 2: Assumption Method 1. Let the original side of the square be 10 units. 2. Original Area = side * side = 10 * 10 = 100 sq units. 3. The side is increased by 25%. New side = 10 + (25% of 10) = 10 + 2.5 = 12.5 units. 4. New Area = 12.5 * 12.5 = 156.25 sq units. 5. Increase in Area = New Area - Original Area = 156.25 - 100 = 56.25 sq units. 6. Percentage Increase = (Increase / Original Area) * 100 = (56.25 / 100) * 100 = 56.25%. Comparing this result to the options: - Option (a) 65.25% is incorrect. - Option (b) 56.25% is correct. - Option (c) 65% is incorrect. - Option (d) 56% is incorrect.

Step-by-step solution: 1. **Determine A's efficiency**: A can complete the job in 15 days. Therefore, A's work rate (efficiency) is 1/15 of the job per day. 2. **Determine B's efficiency**: The problem states that B is twice as fast as A. This means B's efficiency is 2 times that of A. B's efficiency = 2 * (1/15) = 2/15 of the job per day. 3. **Calculate combined efficiency**: When A and B work together, their combined work rate is the sum of their individual rates. Combined rate = (1/15) + (2/15) = 3/15. 4. **Simplify the combined rate**: 3/15 simplifies to 1/5 of the job per day. 5. **Calculate total days**: The time taken to complete the job is the reciprocal of the combined work rate. Time = 1 / (1/5) = 5 days. Comparing with options: - a. 3 days: Incorrect. - b. 8 days: Incorrect. - c. 10 days: Incorrect. - d. 5 days: Correct.

Step-by-step calculation: 1. Calculate 60% of 90: (60/100) * 90 = 0.6 * 90 = 54. 2. Calculate 5% of 20: (5/100) * 20 = 0.05 * 20 = 1. 3. Find the difference to determine how much greater the first value is than the second: 54 - 1 = 53. Reviewing the provided options: a. 12 b. 23 c. 30 d. 38 None of the provided options match the mathematically correct answer of 53. There may be a typo in the question's options provided in the prompt.

Digital citizenship refers to the responsible, ethical, and safe use of technology. 1. Option (b) 'Respecting others’ privacy online' is a core pillar of digital citizenship. It involves understanding boundaries, obtaining consent before sharing others' information, and maintaining confidentiality, which fosters a safe and respectful digital community. 2. Option (a) 'Sharing false information' (misinformation/disinformation) is irresponsible as it can lead to panic, confusion, and social harm. 3. Option (c) 'Cyberbullying' is a violation of digital ethics and is often illegal, involving the harassment of individuals via digital platforms. 4. Option (d) 'Piracy' is the unauthorized use or reproduction of copyrighted material, which is an illegal act and a breach of intellectual property rights. Therefore, only option (b) represents a positive and responsible behavior in the digital world.

To find what percent one number is of another, we use the formula: (Part / Whole) × 100. Step 1: Identify the 'Part' and the 'Whole'. Part = 35 Whole = 70 Step 2: Set up the fraction: 35 / 70. Step 3: Simplify the fraction: 35/70 = 1/2. Step 4: Convert the fraction to a percentage: (1/2) × 100 = 50%. Reviewing the provided options: a. 40% b. 30% c. 20% d. 10% None of the provided options (a, b, c, or d) are correct, as the mathematically accurate answer is 50%.

From the bar graph, take the numbers of girls and boys for the years 2021, 2022, 2023 and 2024. Let the totals be: - Girls = G2021 + G2022 + G2023 + G2024 - Boys = B2021 + B2022 + B2023 + B2024 The ratio of the average number of girls to the average number of boys for 2021–2024 is (G2021 + G2022 + G2023 + G2024)/4 : (B2021 + B2022 + B2023 + B2024)/4 The 4 cancels, so this is simply: Total girls : Total boys Reading the values from the bar graph and adding them gives: - Total girls = 44 - Total boys = 52 So the required ratio is: 44 : 52 = 11 : 13 Therefore, the correct option is (a) 11:13. Why the others are incorrect: - (b) 13:11 is the reverse of the correct ratio. - (c) 11:15 does not match the totals from the graph. - (d) 15:11 is also the reverse/mismatched ratio and not supported by the data.

Option B is correct: 144.

In a pie chart, the full circle represents 100% and the total central angle is 360°. So the central angle for any sector is: central angle = (percentage share / 100) × 360° From the pie-chart, cement corresponds to 20% of the total expenditure. Therefore: central angle = (20/100) × 360° = 72° So the correct option is (d) 72°. Why the other options are incorrect: - (a) 60° would correspond to 16.67% of the total, not 20%. - (b) 62° does not match any standard percentage sector here. - (c) 70° would correspond to 19.44%, which is not the given share. Hence, the correct answer is 72°.

Step-by-step solution: 1. **Identify the given values**: - Ratio of coins (50P : 25P : 10P) = 5 : 9 : 4 - Total amount = Rs. 206 2. **Convert the total amount to Paise** (since coin values are in paise): - Total amount = 206 * 100 = 20,600 Paise 3. **Set up an equation based on the ratio**: Let the number of coins be 5x, 9x, and 4x respectively. - Value of 50P coins = 50 * 5x = 250x - Value of 25P coins = 25 * 9x = 225x - Value of 10P coins = 10 * 4x = 40x 4. **Solve for x**: - 250x + 225x + 40x = 20,600 - 515x = 20,600 - x = 20,600 / 515 - x = 40 5. **Calculate the number of coins of each type**: - 50P coins = 5 * 40 = 200 - 25P coins = 9 * 40 = 360 - 10P coins = 4 * 40 = 160 6. **Verification**: - (200 * 0.50) + (360 * 0.25) + (160 * 0.10) = 100 + 90 + 16 = Rs. 206. The calculation is correct. Comparing this result with the options: Option (c) matches 200, 360, 160.

To solve the expression '45% of 750 - 25% of 480', we follow these steps: Step 1: Calculate 45% of 750. 45% of 750 = (45 / 100) * 750 = 0.45 * 750 = 337.50 Step 2: Calculate 25% of 480. 25% of 480 = (25 / 100) * 480 = 1/4 * 480 = 120 Step 3: Subtract the second result from the first result. 337.50 - 120 = 217.50 Comparing this result to the options: - Option (a) 337.50 is only the first part of the calculation. - Option (b) 217.50 matches our calculated result. - Option (c) 376.21 is mathematically incorrect. - Option (d) 120 is only the second part of the calculation.

Step-by-step reasoning: 1. Analysis of the definition: The question describes the process of changing the 'visual styles' and 'layout elements' to improve 'appearance and readability'. 2. Evaluating 'Formatting': In MS Word, formatting refers to the process of changing the way text and pages look. This includes character formatting (font size, color, bold/italic), paragraph formatting (alignment, line spacing, indentation), and page formatting (margins, orientation). This matches the question perfectly. 3. Evaluating 'Proofing': Proofing refers to checking the document for spelling, grammar, and punctuation errors (e.g., using the Spelling & Grammar tool). It does not deal with visual styles. 4. Evaluating 'Editing': Editing is the process of changing the actual content of the document—adding, deleting, or rearranging text. While it may involve formatting, the act of changing the content is distinct from changing the appearance. 5. Evaluating 'Styling': While 'Styles' are a feature in MS Word used to apply a set of formatting options quickly, 'Formatting' is the broader, overarching term for the process described in the question. Styling is a method of formatting, but formatting is the process itself.

Step-by-step solution: 1. **Identify the given ratio**: The ratio of Cost Price (CP) to Selling Price (SP) is given as 20 : 23. 2. **Assign values**: Let the Cost Price (CP) be 20 units and the Selling Price (SP) be 23 units. 3. **Calculate Profit**: Profit = Selling Price - Cost Price = 23 - 20 = 3 units. 4. **Calculate Profit Percentage**: The formula for profit percentage is (Profit / Cost Price) × 100. Profit % = (3 / 20) × 100 5. **Simplify**: 3 × (100 / 20) = 3 × 5 = 15%. Verification of options: - Option (a) 10% is incorrect as it would require a profit of 2 units (22/20). - Option (b) 15% is correct. - Option (c) 20% is incorrect as it would require a profit of 4 units (24/20). - Option (d) 25% is incorrect as it would require a profit of 5 units (25/20).

To solve the expression 25^0.25 x 25^0.25, we use the laws of exponents. 1. **Law of Exponents**: When multiplying two powers with the same base, we add their exponents: a^m * a^n = a^(m+n). 2. **Application**: Here, the base is 25 and the exponents are 0.25 and 0.25. 25^0.25 * 25^0.25 = 25^(0.25 + 0.25) 3. **Simplification**: 0.25 + 0.25 = 0.50 (or 1/2). So, the expression becomes 25^0.5. 4. **Evaluation**: An exponent of 0.5 is equivalent to the square root of the number. 25^0.5 = √25 = 5. Comparing this to the options: - Option (a) √5 is incorrect. - Option (b) 5 is correct. - Option (c) 25 is incorrect. - Option (d) 5 is also listed as 5, but (b) is the primary correct choice.

HTTP status codes are divided into five classes of responses. The 4xx class is used for Client Error responses. Specifically, the '404 Not Found' status code is issued when the server cannot find the requested resource (e.g., the page has been deleted or the URL was mistyped). Analysis of other options: - a. 200 OK: This is a Success code indicating that the request was successful and the server returned the requested data. - c. 301 Moved Permanently: This is a Redirection code indicating that the resource has been permanently moved to a new URL. - d. 500 Internal Server Error: This is a Server Error code indicating that the server encountered an unexpected condition that prevented it from fulfilling the request, regardless of whether the resource exists.